A device for cooling drinks is described in International Patent Application No.: PCT/NL2008/050068. Using this device, a drink, such as a milkshake, can be cooled quickly and effectively by mixing the drink with a dosed quantity of liquid cryogenic cooling medium, in particular, liquid nitrogen. In order to prevent instant freezing of the drink, a vortex is created in the drink by means of stirring during addition of the cooling medium to the drink. In addition to the method of adding the cryogenic cooling medium to the drink, the periodic cleaning of such a device also represents a critical process. There is a need to optimize this cleaning process, whereby cleaning of the supply conduit can take place in a relatively simple and efficient manner.